Hello, clp_53!
$\displaystyle y\:=\:A ^ {x2}  3\quad A> 1 $
Find: the domain, range, and asymptote(s) ... then sketch.
i got: .$\displaystyle \begin{Bmatrix}\text{Domain:} & \text{all real x} \\\text{Range:} & y \,>\, 3 \\\text{Asymptote:} & y = 3 \end{Bmatrix}$ . . . . Right! We're expected to know the graph of $\displaystyle y \:=\:A^x,\;\;A > 1$ Code:
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It has yintercept (0,1).
To the left, it approaches the xaxis.
To the right, it soars upward.
$\displaystyle y \:=\:A^{x{\color{red}2}}$ .is the same graph moved 2 units to the right.
Then: .$\displaystyle y \:=\:A^{x2} \,{\color{red}\, 3}$ .moves it 3 units down.
Got it?